Below you will find **MCQ Questions of Chapter 11 Circle, Parabola, Ellipse and Hyperbola Class 11 Maths Free PDF Download** that will help you in gaining good marks in the examinations and also cracking competitive exams. These Class 11 MCQ Questions with answers will widen your skills and understand concepts in a better manner.

# MCQ Questions for Class 11 Maths Chapter 11 Circle, Parabola, Ellipse and Hyperbola with answers

1. Which one of the following equations represents parametrically, parabolic profile ?

(a) x = 3 cost ; y = 4 sint

(b) x^{2} – 2 = – cost ; y = 4 cos^{2} t/2

(c) √x = tan t ; √y = sec t

(d) x = ; y = sin t/2 + cos 1/2

► (b) x^{2} – 2 = – cost ; y = 4 cos^{2} t/2

2. The equation 9x^{2} - 16y^{2} - 18x + 32y - 15 = 0 represent a hyperbola

(a) The length of the transverse axes is 4

(b) Length of latus rectum is 9

(c) Equation of directrix is x = 21/5 and x = -1/5

(d) None of these

► (c) Equation of directrix is x = 21/5 and x = -1/5

3. An ellipse is such that the length of the latus rectum is equal to the sum of the lengths of its semi principal axes. Then

(a) Ellipse becomes a circle

(b) Ellipse becomes a line segment between the two foci

(c) Ellipse becomes a parabola

(d) None of these

► (a) Ellipse becomes a circle

4. An ellipse is sliding along the co-ordinate axes. If the foci of the ellipse are (1,1) and (3,3), then area of the director circle of the ellipse (in sq. units) is

(a) 2π

(b) 4π

(c) 6π

(d) 8π

► (d) 8π

5. The tangents to the parabola x = y^{2} + c from origin are perpendicular then c is equal to

(a) 1/2

(b) 1

(c) 2

(d) 1/4

► (d) 1/4

5. The equation of the line passing through the centre and bisecting the chord 7x +y -1 = 0 of the ellipse

(a) x = y

(b) 2x = y

(c) x = 2y

(d) x +y = 0

► (a) x = y

6. Variable circles are drawn touching two fixed circles externally then locus of centre of variable circle is

(a) Parabola

(b) Ellipse

(c) Hyperbola

(d) Circle

► (c) Hyperbola

7. If the tangent at the point P (x_{1}, y_{1}) to the parabola y^{2} = 4ax meets the parabola y^{2} = 4a (x + b) at Q & R, then the mid point of QR is

(a) (x_{1} + b, y_{1} + b)

(b) (x_{1} - b, y_{1} - b)

(c) (x_{1}, y_{1})

(d) (x_{1} + b, y_{1})

► (c) (x_{1}, y_{1})

8. The equation of circle of radius 5 units touches the coordinates axes in the second quadrant is:

(a) x^{2} + y^{2} + 10x – 10y + 25 = 0

(b) x^{2} + y^{2} – 10x – 10y + 25 = 0

(c) x^{2} + y^{2} + 10x + 10y + 25 = 0

(d) x^{2} + y^{2} – 10x – 10y – 25 = 0

► (a) x^{2} + y^{2} + 10x – 10y + 25 = 0

9. The equation of circle whose centre is (2, 1) and which passes through the point (3, – 5) is:

(a) x^{2} + y^{2} - 4x - 2y - 5 = 0

(b) x^{2} + y^{2} - 4x - 2y - 32 = 0

(c) x^{2} + y2 - 4x - 2y - 13 = 0

(d) x^{2} + y^{2} - 4x - 2y - 18 = 0

► (b) x^{2} + y^{2} - 4x - 2y - 32 = 0

10. The equation of the ellipse whose axes are coincident with the co-ordinates axes and which touches the straight lines 3x - 2y - 20 = 0 and x + 6y - 20 = 0 is

(a)

(b)

(c)

(d)

► (a)

11. The tangent to the hyperbola xy = c^{2} at the point P intersects the x-axis at T and the y-axis at T'. The normal to the hyperbola at P intersects the x-axis at N and the y-axis at N'. The areas of the triangles PNT and PNT' are D and D' respectively, then 1/△ + 1/△' is

(a) Equal to 1

(b) Depends on t

(c) Depends on c

(d) Equal to 2

► (c) Depends on c

12. The equation of the circle drawn with the focus of the parabola (x – 1)^{2} – 8y = 0 as its centre and touching the parabola at its vertex is

(a) x^{2} + y^{2} – 4y = 0

(b) x^{2} + y^{2} – 4y + 1 = 0

(c) x^{2} + y^{2} – 2x – 4y = 0

(d) x^{2} + y^{2} – 2x – 4y + 1 = 0

► (d) x^{2} + y^{2} – 2x – 4y + 1 = 0

13. The equation of a circle with centre as the origin is

(a) x^{2} + y^{2} = r^{2}

(b) (y)^{2} = ax

(c) (x-a)^{2} + (y-b)^{2} = r^{2}, where a and b are positive integers

(d) (x)^{2} = ay

► (a) x^{2} + y^{2} = r^{2}

14. The radius of the largest circle whose centre at (-3,0) and is inscribed in the ellipse 16x2 + 25y2 = 400 is

(a) 2

(b) 3

(c) 4

(d) 1

► (a) 2

15. An ellipse with major and minor axes, 6√3 and 6 respectively slides along the coordinate axes and always remains confined in the first quadrant. If the length of arc described by the centre of the ellipse is kπ/6 then the value of k is

(a) 6

(b) 3

(c) 9

(d) 4

► (a) 6

16. The centre and radius of the circle x^{2} + y^{2} + 4x – 6y = 5 is:

(a) (2, – 3), 2√2

(b) (2, – 3), 3√2

(c) (– 2, 3), 2√2

(d) (– 2, 3), 3√2

► (d) (– 2, 3), 3√2

17. The length of the major axis of the ellipse (5x - 10)^{2} + (5y + 15)2 = (3x + 4y + 7)^{2}/4 is

(a) 10

(b) 20/3

(c) 20/7

(d) 4

► (b) 20/3

18. The center of the ellipse (x + y – 2)^{2} /9 + (x – y)^{2} /16 = 1 is

(a) (0, 0)

(b) (0, 1)

(c) (1, 0)

(d) (1, 1)

► (d) (1, 1)

19. At what point of the parabola x^{2} = 9y is the abscissa three times that of ordinate

(a) (1, 1)

(b) (3, 1)

(c) (-3, 1)

(d) (-3, -3)

► (b) (3, 1)

20. If the line x + y – 1 = 0 touches the parabola y^{2} = kx , then the value of k is

(a) 4

(b) –4

(c) 2

(d) –2

► (b) –4

21. The line passing through the extremely A of the major axis and extremity B of the minor axis of the ellipse x^{2} + 9y^{2} = 9 meets its auxiliary circle at the point M . Then the area of the triangle with vertices at A,M and the origin O is

(a) 31/10

(b) 29/10

(c) 21/10

(d) 27/10

► (d) 27/10

22. The equation of parabola with vertex (-2, 1) and focus (-2, 4) is

(a) 10y = x^{2} + 4x + 16

(b) 12y = x^{2} + 4x + 16

(c) 12y = x^{2} + 4x

(d) 12y = x^{2} + 4x + 8

► (b) 12y = x^{2} + 4x + 16

Hope the given MCQ Questions will help you in cracking exams with good marks. These **Parabola, Ellipse and Hyperbola MCQ Questions** will help you in practising more and more questions in less time.